Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1440,3,Mod(1279,1440)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1440, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1440.1279");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1440 = 2^{5} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1440.j (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(39.2371580679\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.1827904.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 14x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 160) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1279.3 | ||
Root | \(1.37720i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1440.1279 |
Dual form | 1440.3.j.b.1279.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1440\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(991\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.54778 | − | 4.75441i | 0.309556 | − | 0.950881i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.206625 | −0.0295178 | −0.0147589 | − | 0.999891i | \(-0.504698\pi\) | ||||
−0.0147589 | + | 0.999891i | \(0.504698\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 15.0176i | − | 1.36524i | −0.730774 | − | 0.682619i | \(-0.760841\pi\) | ||
0.730774 | − | 0.682619i | \(-0.239159\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 11.6999i | − | 0.899995i | −0.893030 | − | 0.449998i | \(-0.851425\pi\) | ||
0.893030 | − | 0.449998i | \(-0.148575\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.1911i | 1.07007i | 0.844831 | + | 0.535033i | \(0.179701\pi\) | ||||
−0.844831 | + | 0.535033i | \(0.820299\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 19.3999i | − | 1.02105i | −0.859864 | − | 0.510523i | \(-0.829452\pi\) | ||
0.859864 | − | 0.510523i | \(-0.170548\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 27.2242 | 1.18366 | 0.591831 | − | 0.806062i | \(-0.298405\pi\) | ||||
0.591831 | + | 0.806062i | \(0.298405\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −20.2087 | − | 14.7176i | −0.808350 | − | 0.588702i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −44.4175 | −1.53164 | −0.765819 | − | 0.643056i | \(-0.777666\pi\) | ||||
−0.765819 | + | 0.643056i | \(0.777666\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 20.3822i | 0.657492i | 0.944418 | + | 0.328746i | \(0.106626\pi\) | ||||
−0.944418 | + | 0.328746i | \(0.893374\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.319810 | + | 0.982377i | −0.00913742 | + | 0.0280679i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 18.1089i | − | 0.489431i | −0.969595 | − | 0.244715i | \(-0.921305\pi\) | ||
0.969595 | − | 0.244715i | \(-0.0786945\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 32.3043 | 0.787910 | 0.393955 | − | 0.919130i | \(-0.371107\pi\) | ||||
0.393955 | + | 0.919130i | \(0.371107\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.06244 | −0.0944753 | −0.0472377 | − | 0.998884i | \(-0.515042\pi\) | ||||
−0.0472377 | + | 0.998884i | \(0.515042\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.37588 | −0.114380 | −0.0571902 | − | 0.998363i | \(-0.518214\pi\) | ||||
−0.0571902 | + | 0.998363i | \(0.518214\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.9573 | −0.999129 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 79.1703i | 1.49378i | 0.664948 | + | 0.746890i | \(0.268454\pi\) | ||||
−0.664948 | + | 0.746890i | \(0.731546\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −71.3999 | − | 23.2440i | −1.29818 | − | 0.422618i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 83.3999i | − | 1.41356i | −0.707435 | − | 0.706779i | \(-0.750148\pi\) | ||
0.707435 | − | 0.706779i | \(-0.249852\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −36.7486 | −0.602435 | −0.301218 | − | 0.953555i | \(-0.597393\pi\) | ||||
−0.301218 | + | 0.953555i | \(0.597393\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −55.6262 | − | 18.1089i | −0.855788 | − | 0.278599i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.51518 | −0.0673907 | −0.0336954 | − | 0.999432i | \(-0.510728\pi\) | ||||
−0.0336954 | + | 0.999432i | \(0.510728\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 41.6530i | − | 0.586662i | −0.956011 | − | 0.293331i | \(-0.905236\pi\) | ||
0.956011 | − | 0.293331i | \(-0.0947638\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 41.5910i | 0.569740i | 0.958566 | + | 0.284870i | \(0.0919504\pi\) | ||||
−0.958566 | + | 0.284870i | \(0.908050\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.10301i | 0.0402988i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 15.5473i | − | 0.196801i | −0.995147 | − | 0.0984004i | \(-0.968627\pi\) | ||
0.995147 | − | 0.0984004i | \(-0.0313726\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 50.9862 | 0.614291 | 0.307146 | − | 0.951663i | \(-0.400626\pi\) | ||||
0.307146 | + | 0.951663i | \(0.400626\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 86.4880 | + | 28.1559i | 1.01751 | + | 0.331246i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −10.8885 | −0.122343 | −0.0611713 | − | 0.998127i | \(-0.519484\pi\) | ||||
−0.0611713 | + | 0.998127i | \(0.519484\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.41749i | 0.0265659i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −92.2349 | − | 30.0268i | −0.970893 | − | 0.316071i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 12.1559i | − | 0.125318i | −0.998035 | − | 0.0626592i | \(-0.980042\pi\) | ||
0.998035 | − | 0.0626592i | \(-0.0199581\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −127.723 | −1.26459 | −0.632294 | − | 0.774728i | \(-0.717887\pi\) | ||||
−0.632294 | + | 0.774728i | \(0.717887\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.77575 | 0.0463665 | 0.0231833 | − | 0.999731i | \(-0.492620\pi\) | ||||
0.0231833 | + | 0.999731i | \(0.492620\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −107.213 | −1.00199 | −0.500997 | − | 0.865449i | \(-0.667033\pi\) | ||||
−0.500997 | + | 0.865449i | \(0.667033\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 53.6689 | 0.492376 | 0.246188 | − | 0.969222i | \(-0.420822\pi\) | ||||
0.246188 | + | 0.969222i | \(0.420822\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 20.5063i | − | 0.181471i | −0.995875 | − | 0.0907356i | \(-0.971078\pi\) | ||
0.995875 | − | 0.0907356i | \(-0.0289218\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 42.1372 | − | 129.435i | 0.366410 | − | 1.12552i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 3.75873i | − | 0.0315860i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −104.529 | −0.863876 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −101.252 | + | 73.3010i | −0.810016 | + | 0.586408i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −138.477 | −1.09037 | −0.545184 | − | 0.838316i | \(-0.683540\pi\) | ||||
−0.545184 | + | 0.838316i | \(0.683540\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 219.105i | − | 1.67256i | −0.548304 | − | 0.836279i | \(-0.684726\pi\) | ||
0.548304 | − | 0.836279i | \(-0.315274\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00849i | 0.0301390i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 59.7821i | 0.436366i | 0.975908 | + | 0.218183i | \(0.0700129\pi\) | ||||
−0.975908 | + | 0.218183i | \(0.929987\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 26.6524i | − | 0.191744i | −0.995394 | − | 0.0958718i | \(-0.969436\pi\) | ||
0.995394 | − | 0.0958718i | \(-0.0305639\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −175.705 | −1.22871 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −68.7486 | + | 211.179i | −0.474128 | + | 1.45641i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −143.463 | −0.962838 | −0.481419 | − | 0.876490i | \(-0.659879\pi\) | ||||
−0.481419 | + | 0.876490i | \(0.659879\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 83.4937i | 0.552939i | 0.961023 | + | 0.276469i | \(0.0891644\pi\) | ||||
−0.961023 | + | 0.276469i | \(0.910836\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 96.9055 | + | 31.5473i | 0.625197 | + | 0.203531i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 169.673i | 1.08072i | 0.841434 | + | 0.540360i | \(0.181712\pi\) | ||||
−0.841434 | + | 0.540360i | \(0.818288\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.62520 | −0.0349391 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 275.478 | 1.69005 | 0.845026 | − | 0.534726i | \(-0.179585\pi\) | ||||
0.845026 | + | 0.534726i | \(0.179585\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −132.481 | −0.793299 | −0.396650 | − | 0.917970i | \(-0.629827\pi\) | ||||
−0.396650 | + | 0.917970i | \(0.629827\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 32.1115 | 0.190009 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 272.614i | − | 1.57580i | −0.615801 | − | 0.787901i | \(-0.711168\pi\) | ||
0.615801 | − | 0.787901i | \(-0.288832\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.17562 | + | 3.04101i | 0.0238607 | + | 0.0173772i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 157.523i | 0.880014i | 0.897994 | + | 0.440007i | \(0.145024\pi\) | ||||
−0.897994 | + | 0.440007i | \(0.854976\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −335.063 | −1.85118 | −0.925590 | − | 0.378529i | \(-0.876430\pi\) | ||||
−0.925590 | + | 0.378529i | \(0.876430\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −86.0972 | − | 28.0287i | −0.465391 | − | 0.151506i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 273.187 | 1.46090 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 298.575i | − | 1.56322i | −0.623766 | − | 0.781611i | \(-0.714398\pi\) | ||
0.623766 | − | 0.781611i | \(-0.285602\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 191.915i | − | 0.994376i | −0.867643 | − | 0.497188i | \(-0.834366\pi\) | ||
0.867643 | − | 0.497188i | \(-0.165634\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 59.2472i | − | 0.300747i | −0.988629 | − | 0.150374i | \(-0.951952\pi\) | ||
0.988629 | − | 0.150374i | \(-0.0480477\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 309.100i | − | 1.55327i | −0.629953 | − | 0.776633i | \(-0.716926\pi\) | ||
0.629953 | − | 0.776633i | \(-0.283074\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.17775 | 0.0452106 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 50.0000 | − | 153.588i | 0.243902 | − | 0.749209i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −291.340 | −1.39397 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 205.693i | − | 0.974850i | −0.873165 | − | 0.487425i | \(-0.837936\pi\) | ||
0.873165 | − | 0.487425i | \(-0.162064\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.28777 | + | 19.3145i | −0.0292454 | + | 0.0898348i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 4.21147i | − | 0.0194077i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 212.835 | 0.963054 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −228.723 | −1.02567 | −0.512833 | − | 0.858488i | \(-0.671404\pi\) | ||||
−0.512833 | + | 0.858488i | \(0.671404\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 282.403 | 1.24407 | 0.622033 | − | 0.782991i | \(-0.286307\pi\) | ||||
0.622033 | + | 0.782991i | \(0.286307\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 49.2525 | 0.215076 | 0.107538 | − | 0.994201i | \(-0.465703\pi\) | ||||
0.107538 | + | 0.994201i | \(0.465703\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 124.273i | − | 0.533363i | −0.963785 | − | 0.266681i | \(-0.914073\pi\) | ||
0.963785 | − | 0.266681i | \(-0.0859271\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.32069 | + | 25.5591i | −0.0354072 | + | 0.108762i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 80.4527i | − | 0.336622i | −0.985734 | − | 0.168311i | \(-0.946169\pi\) | ||
0.985734 | − | 0.168311i | \(-0.0538313\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.20979 | −0.00501988 | −0.00250994 | − | 0.999997i | \(-0.500799\pi\) | ||||
−0.00250994 | + | 0.999997i | \(0.500799\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −75.7752 | + | 232.763i | −0.309287 | + | 0.950053i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −226.977 | −0.918936 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 211.853i | − | 0.844034i | −0.906588 | − | 0.422017i | \(-0.861322\pi\) | ||
0.906588 | − | 0.422017i | \(-0.138678\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 408.843i | − | 1.61598i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 182.646i | 0.710685i | 0.934736 | + | 0.355342i | \(0.115636\pi\) | ||||
−0.934736 | + | 0.355342i | \(0.884364\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.74175i | 0.0144469i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −74.6636 | −0.283892 | −0.141946 | − | 0.989874i | \(-0.545336\pi\) | ||||
−0.141946 | + | 0.989874i | \(0.545336\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 376.408 | + | 122.538i | 1.42041 | + | 0.462409i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 184.089 | 0.684344 | 0.342172 | − | 0.939637i | \(-0.388837\pi\) | ||||
0.342172 | + | 0.939637i | \(0.388837\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 234.746i | 0.866222i | 0.901341 | + | 0.433111i | \(0.142584\pi\) | ||||
−0.901341 | + | 0.433111i | \(0.857416\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −221.023 | + | 303.487i | −0.803719 | + | 1.10359i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 452.208i | 1.63252i | 0.577684 | + | 0.816260i | \(0.303957\pi\) | ||||
−0.577684 | + | 0.816260i | \(0.696043\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 196.110 | 0.697900 | 0.348950 | − | 0.937141i | \(-0.386538\pi\) | ||||
0.348950 | + | 0.937141i | \(0.386538\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 418.449 | 1.47862 | 0.739309 | − | 0.673366i | \(-0.235152\pi\) | ||||
0.739309 | + | 0.673366i | \(0.235152\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.67486 | −0.0232574 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −41.9170 | −0.145042 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 286.666i | 0.978383i | 0.872176 | + | 0.489191i | \(0.162708\pi\) | ||||
−0.872176 | + | 0.489191i | \(0.837292\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −396.517 | − | 129.085i | −1.34412 | − | 0.437575i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 318.522i | − | 1.06529i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.839400 | 0.00278870 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −56.8787 | + | 174.718i | −0.186488 | + | 0.572844i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −261.715 | −0.852493 | −0.426247 | − | 0.904607i | \(-0.640164\pi\) | ||||
−0.426247 | + | 0.904607i | \(0.640164\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 578.904i | 1.86143i | 0.365747 | + | 0.930714i | \(0.380813\pi\) | ||||
−0.365747 | + | 0.930714i | \(0.619187\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 99.3124i | − | 0.317292i | −0.987336 | − | 0.158646i | \(-0.949287\pi\) | ||
0.987336 | − | 0.158646i | \(-0.0507129\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 191.623i | − | 0.604489i | −0.953230 | − | 0.302245i | \(-0.902264\pi\) | ||
0.953230 | − | 0.302245i | \(-0.0977359\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 667.045i | 2.09105i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 352.905 | 1.09259 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −172.194 | + | 236.441i | −0.529829 | + | 0.727511i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.11079 | 0.00337626 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 530.187i | 1.60177i | 0.598816 | + | 0.800886i | \(0.295638\pi\) | ||||
−0.598816 | + | 0.800886i | \(0.704362\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.98851 | + | 21.4670i | −0.0208612 | + | 0.0640806i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 487.427i | − | 1.44637i | −0.690653 | − | 0.723186i | \(-0.742677\pi\) | ||
0.690653 | − | 0.723186i | \(-0.257323\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 306.093 | 0.897633 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.2404 | 0.0590099 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 310.497 | 0.894804 | 0.447402 | − | 0.894333i | \(-0.352349\pi\) | ||||
0.447402 | + | 0.894333i | \(0.352349\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −253.004 | −0.724941 | −0.362471 | − | 0.931995i | \(-0.618067\pi\) | ||||
−0.362471 | + | 0.931995i | \(0.618067\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 322.639i | − | 0.913992i | −0.889469 | − | 0.456996i | \(-0.848925\pi\) | ||
0.889469 | − | 0.456996i | \(-0.151075\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −198.035 | − | 64.4697i | −0.557846 | − | 0.181605i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 254.975i | 0.710236i | 0.934822 | + | 0.355118i | \(0.115559\pi\) | ||||
−0.934822 | + | 0.355118i | \(0.884441\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.3550 | −0.0425347 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 197.740 | + | 64.3738i | 0.541755 | + | 0.176366i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −207.935 | −0.566581 | −0.283291 | − | 0.959034i | \(-0.591426\pi\) | ||||
−0.283291 | + | 0.959034i | \(0.591426\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 16.3585i | − | 0.0440931i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 203.826i | − | 0.546450i | −0.961950 | − | 0.273225i | \(-0.911910\pi\) | ||
0.961950 | − | 0.273225i | \(-0.0880903\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 519.682i | 1.37847i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 454.099i | − | 1.19815i | −0.800692 | − | 0.599076i | \(-0.795535\pi\) | ||
0.800692 | − | 0.599076i | \(-0.204465\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 541.569 | 1.41402 | 0.707009 | − | 0.707205i | \(-0.250044\pi\) | ||||
0.707009 | + | 0.707205i | \(0.250044\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 14.7530 | + | 4.80278i | 0.0383194 | + | 0.0124748i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 423.431 | 1.08851 | 0.544256 | − | 0.838919i | \(-0.316812\pi\) | ||||
0.544256 | + | 0.838919i | \(0.316812\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 495.240i | 1.26660i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −73.9180 | − | 24.0638i | −0.187134 | − | 0.0609209i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 11.7772i | − | 0.0296654i | −0.999890 | − | 0.0148327i | \(-0.995278\pi\) | ||
0.999890 | − | 0.0148327i | \(-0.00472157\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −127.442 | −0.317809 | −0.158905 | − | 0.987294i | \(-0.550796\pi\) | ||||
−0.158905 | + | 0.987294i | \(0.550796\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 238.471 | 0.591739 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −271.953 | −0.668190 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 608.012 | 1.48658 | 0.743290 | − | 0.668969i | \(-0.233264\pi\) | ||||
0.743290 | + | 0.668969i | \(0.233264\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 17.2325i | 0.0417251i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 78.9155 | − | 242.409i | 0.190158 | − | 0.584118i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 565.630i | 1.34995i | 0.737840 | + | 0.674976i | \(0.235846\pi\) | ||||
−0.737840 | + | 0.674976i | \(0.764154\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 711.356 | 1.68968 | 0.844841 | − | 0.535018i | \(-0.179695\pi\) | ||||
0.844841 | + | 0.535018i | \(0.179695\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 267.729 | − | 367.620i | 0.629950 | − | 0.864988i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.59316 | 0.0177826 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 309.254i | 0.717526i | 0.933429 | + | 0.358763i | \(0.116801\pi\) | ||||
−0.933429 | + | 0.358763i | \(0.883199\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 187.374i | − | 0.432735i | −0.976312 | − | 0.216368i | \(-0.930579\pi\) | ||
0.976312 | − | 0.216368i | \(-0.0694210\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 528.147i | − | 1.20857i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 289.657i | − | 0.659811i | −0.944014 | − | 0.329906i | \(-0.892983\pi\) | ||
0.944014 | − | 0.329906i | \(-0.107017\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 295.516 | 0.667079 | 0.333539 | − | 0.942736i | \(-0.391757\pi\) | ||||
0.333539 | + | 0.942736i | \(0.391757\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.8530 | + | 51.7683i | −0.0378719 | + | 0.116333i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 604.409 | 1.34612 | 0.673061 | − | 0.739587i | \(-0.264979\pi\) | ||||
0.673061 | + | 0.739587i | \(0.264979\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 485.134i | − | 1.07569i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.4937 | + | 3.74175i | 0.0252610 | + | 0.00822363i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 392.507i | 0.858877i | 0.903096 | + | 0.429438i | \(0.141288\pi\) | ||||
−0.903096 | + | 0.429438i | \(0.858712\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 400.277 | 0.868279 | 0.434139 | − | 0.900846i | \(-0.357053\pi\) | ||||
0.434139 | + | 0.900846i | \(0.357053\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 732.679 | 1.58246 | 0.791230 | − | 0.611518i | \(-0.209441\pi\) | ||||
0.791230 | + | 0.611518i | \(0.209441\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −592.126 | −1.26794 | −0.633968 | − | 0.773360i | \(-0.718575\pi\) | ||||
−0.633968 | + | 0.773360i | \(0.718575\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.932947 | 0.00198923 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 61.0082i | 0.128981i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −285.519 | + | 392.047i | −0.601092 | + | 0.825362i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 309.151i | 0.645409i | 0.946500 | + | 0.322705i | \(0.104592\pi\) | ||||
−0.946500 | + | 0.322705i | \(0.895408\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −211.873 | −0.440485 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −57.7940 | − | 18.8146i | −0.119163 | − | 0.0387931i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −570.769 | −1.17201 | −0.586005 | − | 0.810307i | \(-0.699300\pi\) | ||||
−0.586005 | + | 0.810307i | \(0.699300\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 301.659i | − | 0.614378i | −0.951649 | − | 0.307189i | \(-0.900612\pi\) | ||
0.951649 | − | 0.307189i | \(-0.0993883\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 808.004i | − | 1.63895i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.60653i | 0.0173170i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 517.758i | 1.03759i | 0.854898 | + | 0.518795i | \(0.173619\pi\) | ||||
−0.854898 | + | 0.518795i | \(0.826381\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 406.671 | 0.808491 | 0.404246 | − | 0.914650i | \(-0.367534\pi\) | ||||
0.404246 | + | 0.914650i | \(0.367534\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −197.688 | + | 607.249i | −0.391461 | + | 1.20247i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −627.097 | −1.23202 | −0.616009 | − | 0.787739i | \(-0.711252\pi\) | ||||
−0.616009 | + | 0.787739i | \(0.711252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 8.59372i | − | 0.0168175i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 7.39182 | − | 22.7059i | 0.0143530 | − | 0.0440891i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 80.7330i | 0.156157i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 111.743 | 0.214478 | 0.107239 | − | 0.994233i | \(-0.465799\pi\) | ||||
0.107239 | + | 0.994233i | \(0.465799\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 769.813 | 1.47192 | 0.735959 | − | 0.677027i | \(-0.236732\pi\) | ||||
0.735959 | + | 0.677027i | \(0.236732\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −370.776 | −0.703560 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 212.160 | 0.401058 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 377.958i | − | 0.709115i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −165.943 | + | 509.736i | −0.310174 | + | 0.952778i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 735.222i | 1.36405i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −225.558 | −0.416927 | −0.208463 | − | 0.978030i | \(-0.566846\pi\) | ||||
−0.208463 | + | 0.978030i | \(0.566846\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 83.0678 | − | 255.164i | 0.152418 | − | 0.468191i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 882.346 | 1.61306 | 0.806532 | − | 0.591190i | \(-0.201342\pi\) | ||||
0.806532 | + | 0.591190i | \(0.201342\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 861.694i | 1.56387i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.21245i | 0.00580913i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 303.119i | − | 0.544199i | −0.962269 | − | 0.272100i | \(-0.912282\pi\) | ||
0.962269 | − | 0.272100i | \(-0.0877180\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 47.5303i | 0.0850273i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 344.003 | 0.611017 | 0.305508 | − | 0.952189i | \(-0.401174\pi\) | ||||
0.305508 | + | 0.952189i | \(0.401174\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −97.4950 | − | 31.7392i | −0.172558 | − | 0.0561756i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 228.925 | 0.402329 | 0.201165 | − | 0.979557i | \(-0.435527\pi\) | ||||
0.201165 | + | 0.979557i | \(0.435527\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 371.169i | − | 0.650033i | −0.945708 | − | 0.325017i | \(-0.894630\pi\) | ||
0.945708 | − | 0.325017i | \(-0.105370\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −550.168 | − | 400.674i | −0.956814 | − | 0.696825i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 580.289i | − | 1.00570i | −0.864374 | − | 0.502850i | \(-0.832285\pi\) | ||
0.864374 | − | 0.502850i | \(-0.167715\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.5350 | −0.0181325 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1188.95 | 2.03936 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −65.0801 | −0.110869 | −0.0554345 | − | 0.998462i | \(-0.517654\pi\) | ||||
−0.0554345 | + | 0.998462i | \(0.517654\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 395.413 | 0.671329 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 1002.90i | − | 1.69124i | −0.533787 | − | 0.845619i | \(-0.679232\pi\) | ||
0.533787 | − | 0.845619i | \(-0.320768\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.8705 | − | 5.81770i | −0.0300345 | − | 0.00977764i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 888.567i | − | 1.48342i | −0.670722 | − | 0.741709i | \(-0.734016\pi\) | ||
0.670722 | − | 0.741709i | \(-0.265984\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 132.065 | 0.219742 | 0.109871 | − | 0.993946i | \(-0.464956\pi\) | ||||
0.109871 | + | 0.993946i | \(0.464956\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −161.788 | + | 496.973i | −0.267418 | + | 0.821443i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 700.090 | 1.15336 | 0.576680 | − | 0.816970i | \(-0.304348\pi\) | ||||
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 62.8975i | 0.102942i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 727.420i | 1.18666i | 0.804961 | + | 0.593328i | \(0.202186\pi\) | ||||
−0.804961 | + | 0.593328i | \(0.797814\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 99.7137i | − | 0.161611i | −0.996730 | − | 0.0808053i | \(-0.974251\pi\) | ||
0.996730 | − | 0.0808053i | \(-0.0257492\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 721.349i | 1.16535i | 0.812707 | + | 0.582673i | \(0.197993\pi\) | ||||
−0.812707 | + | 0.582673i | \(0.802007\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.24983 | 0.00361129 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 191.787 | + | 594.847i | 0.306859 | + | 0.951755i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 329.422 | 0.523723 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 796.856i | − | 1.26285i | −0.775438 | − | 0.631423i | \(-0.782471\pi\) | ||
0.775438 | − | 0.631423i | \(-0.217529\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −214.332 | + | 658.375i | −0.337530 | + | 1.03681i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 572.797i | 0.899211i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −205.013 | −0.319833 | −0.159917 | − | 0.987131i | \(-0.551123\pi\) | ||||
−0.159917 | + | 0.987131i | \(0.551123\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −495.044 | −0.769897 | −0.384949 | − | 0.922938i | \(-0.625781\pi\) | ||||
−0.384949 | + | 0.922938i | \(0.625781\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1121.84 | 1.73391 | 0.866953 | − | 0.498389i | \(-0.166075\pi\) | ||||
0.866953 | + | 0.498389i | \(0.166075\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1252.47 | −1.92984 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 622.987i | − | 0.954038i | −0.878893 | − | 0.477019i | \(-0.841717\pi\) | ||
0.878893 | − | 0.477019i | \(-0.158283\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1041.71 | − | 339.127i | −1.59040 | − | 0.517751i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 264.030i | 0.400653i | 0.979729 | + | 0.200326i | \(0.0642002\pi\) | ||||
−0.979729 | + | 0.200326i | \(0.935800\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1285.15 | 1.94425 | 0.972124 | − | 0.234469i | \(-0.0753352\pi\) | ||||
0.972124 | + | 0.234469i | \(0.0753352\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 19.0580 | + | 6.20427i | 0.0286586 | + | 0.00932972i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1209.23 | −1.81294 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 551.876i | 0.822468i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1244.16i | − | 1.84868i | −0.381565 | − | 0.924342i | \(-0.624615\pi\) | ||
0.381565 | − | 0.924342i | \(-0.375385\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 963.335i | 1.42295i | 0.702713 | + | 0.711473i | \(0.251972\pi\) | ||||
−0.702713 | + | 0.711473i | \(0.748028\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.51170i | 0.00369912i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −770.819 | −1.12858 | −0.564289 | − | 0.825577i | \(-0.690850\pi\) | ||||
−0.564289 | + | 0.825577i | \(0.690850\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 284.228 | + | 92.5296i | 0.414932 | + | 0.135080i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 926.287 | 1.34439 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 408.765i | − | 0.591555i | −0.955257 | − | 0.295778i | \(-0.904421\pi\) | ||
0.955257 | − | 0.295778i | \(-0.0955788\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −126.716 | − | 41.2520i | −0.182325 | − | 0.0593554i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 587.652i | 0.843116i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1335.62 | −1.90530 | −0.952650 | − | 0.304068i | \(-0.901655\pi\) | ||||
−0.952650 | + | 0.304068i | \(0.901655\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −351.311 | −0.499731 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 26.3908 | 0.0373279 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 362.956 | 0.511927 | 0.255964 | − | 0.966686i | \(-0.417607\pi\) | ||||
0.255964 | + | 0.966686i | \(0.417607\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 554.891i | 0.778249i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −271.953 | + | 835.374i | −0.380354 | + | 1.16836i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 648.098i | − | 0.901388i | −0.892679 | − | 0.450694i | \(-0.851177\pi\) | ||
0.892679 | − | 0.450694i | \(-0.148823\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.986788 | −0.00136864 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 897.622 | + | 653.717i | 1.23810 | + | 0.901679i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 431.123 | 0.593017 | 0.296508 | − | 0.955030i | \(-0.404178\pi\) | ||||
0.296508 | + | 0.955030i | \(0.404178\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 73.9003i | − | 0.101095i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1464.87i | − | 1.99846i | −0.0392126 | − | 0.999231i | \(-0.512485\pi\) | ||
0.0392126 | − | 0.999231i | \(-0.487515\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 67.8073i | 0.0920044i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 99.1951i | − | 0.134229i | −0.997745 | − | 0.0671144i | \(-0.978621\pi\) | ||
0.997745 | − | 0.0671144i | \(-0.0213793\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −602.719 | −0.811196 | −0.405598 | − | 0.914052i | \(-0.632937\pi\) | ||||
−0.405598 | + | 0.914052i | \(0.632937\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −222.049 | + | 682.081i | −0.298053 | + | 0.915545i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.1529 | 0.0295767 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 541.472i | 0.721001i | 0.932759 | + | 0.360501i | \(0.117394\pi\) | ||||
−0.932759 | + | 0.360501i | \(0.882606\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 396.963 | + | 129.230i | 0.525779 | + | 0.171166i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1092.79i | 1.44358i | 0.692113 | + | 0.721789i | \(0.256680\pi\) | ||||
−0.692113 | + | 0.721789i | \(0.743320\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 18.7706 | 0.0246657 | 0.0123328 | − | 0.999924i | \(-0.496074\pi\) | ||||
0.0123328 | + | 0.999924i | \(0.496074\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −11.0893 | −0.0145338 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −975.773 | −1.27219 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 39.0830 | 0.0508231 | 0.0254116 | − | 0.999677i | \(-0.491910\pi\) | ||||
0.0254116 | + | 0.999677i | \(0.491910\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 31.2171i | 0.0403843i | 0.999796 | + | 0.0201922i | \(0.00642780\pi\) | ||||
−0.999796 | + | 0.0201922i | \(0.993572\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 299.977 | − | 411.900i | 0.387067 | − | 0.531484i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 626.699i | − | 0.804492i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −625.529 | −0.800933 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 806.695 | + | 262.617i | 1.02764 | + | 0.334544i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −988.563 | −1.25612 | −0.628058 | − | 0.778167i | \(-0.716150\pi\) | ||||
−0.628058 | + | 0.778167i | \(0.716150\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.23710i | 0.00535663i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 429.956i | 0.542189i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 118.920i | 0.149210i | 0.997213 | + | 0.0746048i | \(0.0237695\pi\) | ||||
−0.997213 | + | 0.0746048i | \(0.976230\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 97.7933i | − | 0.122395i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 624.598 | 0.777831 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.70658 | + | 26.7445i | −0.0108156 | + | 0.0332230i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1214.04 | −1.50067 | −0.750337 | − | 0.661056i | \(-0.770109\pi\) | ||||
−0.750337 | + | 0.661056i | \(0.770109\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 706.666i | − | 0.871351i | −0.900104 | − | 0.435676i | \(-0.856509\pi\) | ||
0.900104 | − | 0.435676i | \(-0.143491\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 426.380 | − | 1309.74i | 0.523166 | − | 1.60704i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 78.8108i | 0.0964636i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −991.775 | −1.20801 | −0.604004 | − | 0.796981i | \(-0.706429\pi\) | ||||
−0.604004 | + | 0.796981i | \(0.706429\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 523.998 | 0.636693 | 0.318347 | − | 0.947974i | \(-0.396872\pi\) | ||||
0.318347 | + | 0.947974i | \(0.396872\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −318.794 | −0.385483 | −0.192741 | − | 0.981250i | \(-0.561738\pi\) | ||||
−0.192741 | + | 0.981250i | \(0.561738\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1034.11 | −1.24742 | −0.623711 | − | 0.781655i | \(-0.714376\pi\) | ||||
−0.623711 | + | 0.781655i | \(0.714376\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 890.588i | − | 1.06913i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −205.052 | + | 629.868i | −0.245571 | + | 0.754333i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 445.284i | − | 0.530732i | −0.964148 | − | 0.265366i | \(-0.914507\pi\) | ||
0.964148 | − | 0.265366i | \(-0.0854928\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1131.91 | 1.34591 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 49.7016 | − | 152.671i | 0.0588184 | − | 0.180676i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 21.5983 | 0.0254997 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 493.002i | − | 0.579321i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1200.49i | − | 1.40737i | −0.710513 | − | 0.703684i | \(-0.751537\pi\) | ||
0.710513 | − | 0.703684i | \(-0.248463\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1223.15i | 1.42724i | 0.700531 | + | 0.713622i | \(0.252946\pi\) | ||||
−0.700531 | + | 0.713622i | \(0.747054\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 210.033i | − | 0.244509i | −0.992499 | − | 0.122254i | \(-0.960988\pi\) | ||
0.992499 | − | 0.122254i | \(-0.0390124\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1560.47 | 1.80819 | 0.904095 | − | 0.427333i | \(-0.140547\pi\) | ||||
0.904095 | + | 0.427333i | \(0.140547\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1296.12 | − | 421.947i | −1.49840 | − | 0.487800i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −233.483 | −0.268680 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 52.8273i | 0.0606513i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 20.9211 | − | 15.1458i | 0.0239099 | − | 0.0173095i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 1011.66i | − | 1.15354i | −0.816906 | − | 0.576771i | \(-0.804313\pi\) | ||
0.816906 | − | 0.576771i | \(-0.195687\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −266.455 | −0.302446 | −0.151223 | − | 0.988500i | \(-0.548321\pi\) | ||||
−0.151223 | + | 0.988500i | \(0.548321\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −469.871 | −0.532130 | −0.266065 | − | 0.963955i | \(-0.585724\pi\) | ||||
−0.266065 | + | 0.963955i | \(0.585724\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 764.559 | 0.861961 | 0.430980 | − | 0.902361i | \(-0.358168\pi\) | ||||
0.430980 | + | 0.902361i | \(0.358168\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 28.6127 | 0.0321853 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 104.291i | 0.116788i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 748.926 | + | 243.810i | 0.836789 | + | 0.272414i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 905.328i | − | 1.00704i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1440.20 | −1.59844 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −518.605 | + | 1593.03i | −0.573044 | + | 1.76025i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1333.20 | −1.46990 | −0.734948 | − | 0.678123i | \(-0.762794\pi\) | ||||
−0.734948 | + | 0.678123i | \(0.762794\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1496.11i | 1.64227i | 0.570736 | + | 0.821134i | \(0.306658\pi\) | ||||
−0.570736 | + | 0.821134i | \(0.693342\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 765.691i | − | 0.838654i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 45.2725i | 0.0493702i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 564.228i | − | 0.613959i | −0.951716 | − | 0.306980i | \(-0.900682\pi\) | ||
0.951716 | − | 0.306980i | \(-0.0993183\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −487.337 | −0.527993 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −266.519 | + | 365.959i | −0.288129 | + | 0.395631i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1449.16 | −1.55991 | −0.779957 | − | 0.625833i | \(-0.784759\pi\) | ||||
−0.779957 | + | 0.625833i | \(0.784759\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 949.765i | 1.02016i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 422.834 | − | 1298.84i | 0.452229 | − | 1.38914i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 258.795i | − | 0.276196i | −0.990419 | − | 0.138098i | \(-0.955901\pi\) | ||
0.990419 | − | 0.138098i | \(-0.0440989\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.3444 | −0.0216200 | −0.0108100 | − | 0.999942i | \(-0.503441\pi\) | ||||
−0.0108100 | + | 0.999942i | \(0.503441\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 879.461 | 0.932620 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −613.539 | −0.647876 | −0.323938 | − | 0.946078i | \(-0.605007\pi\) | ||||
−0.323938 | + | 0.946078i | \(0.605007\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 486.612 | 0.512763 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 81.6126i | 0.0856376i | 0.999083 | + | 0.0428188i | \(0.0136338\pi\) | ||||
−0.999083 | + | 0.0428188i | \(0.986366\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1419.55 | − | 462.129i | −1.48644 | − | 0.483905i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 12.3525i | − | 0.0128806i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 545.564 | 0.567704 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −912.440 | − | 297.042i | −0.945534 | − | 0.307815i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −127.482 | −0.131833 | −0.0659165 | − | 0.997825i | \(-0.520997\pi\) | ||||
−0.0659165 | + | 0.997825i | \(0.520997\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1122.62i | − | 1.15615i | −0.815983 | − | 0.578076i | \(-0.803804\pi\) | ||
0.815983 | − | 0.578076i | \(-0.196196\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.50703i | 0.00565985i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 424.837i | − | 0.434838i | −0.976078 | − | 0.217419i | \(-0.930236\pi\) | ||
0.976078 | − | 0.217419i | \(-0.0697639\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 163.519i | 0.167027i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −663.324 | −0.674795 | −0.337398 | − | 0.941362i | \(-0.609547\pi\) | ||||
−0.337398 | + | 0.941362i | \(0.609547\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −281.685 | − | 91.7017i | −0.285975 | − | 0.0930982i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −110.597 | −0.111827 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1771.36i | − | 1.78745i | −0.448616 | − | 0.893724i | \(-0.648083\pi\) | ||
0.448616 | − | 0.893724i | \(-0.351917\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1469.59 | − | 478.419i | −1.47697 | − | 0.480823i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 447.066i | 0.448411i | 0.974542 | + | 0.224205i | \(0.0719786\pi\) | ||||
−0.974542 | + | 0.224205i | \(0.928021\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1440.3.j.b.1279.3 | 6 | ||
3.2 | odd | 2 | 160.3.h.b.159.6 | yes | 6 | ||
4.3 | odd | 2 | 1440.3.j.a.1279.3 | 6 | |||
5.4 | even | 2 | 1440.3.j.a.1279.4 | 6 | |||
12.11 | even | 2 | 160.3.h.a.159.2 | yes | 6 | ||
15.2 | even | 4 | 800.3.b.i.351.1 | 6 | |||
15.8 | even | 4 | 800.3.b.h.351.6 | 6 | |||
15.14 | odd | 2 | 160.3.h.a.159.1 | ✓ | 6 | ||
20.19 | odd | 2 | inner | 1440.3.j.b.1279.4 | 6 | ||
24.5 | odd | 2 | 320.3.h.f.319.1 | 6 | |||
24.11 | even | 2 | 320.3.h.g.319.5 | 6 | |||
48.5 | odd | 4 | 1280.3.e.f.639.1 | 6 | |||
48.11 | even | 4 | 1280.3.e.g.639.6 | 6 | |||
48.29 | odd | 4 | 1280.3.e.h.639.6 | 6 | |||
48.35 | even | 4 | 1280.3.e.i.639.1 | 6 | |||
60.23 | odd | 4 | 800.3.b.h.351.1 | 6 | |||
60.47 | odd | 4 | 800.3.b.i.351.6 | 6 | |||
60.59 | even | 2 | 160.3.h.b.159.5 | yes | 6 | ||
120.29 | odd | 2 | 320.3.h.g.319.6 | 6 | |||
120.53 | even | 4 | 1600.3.b.v.1151.1 | 6 | |||
120.59 | even | 2 | 320.3.h.f.319.2 | 6 | |||
120.77 | even | 4 | 1600.3.b.w.1151.6 | 6 | |||
120.83 | odd | 4 | 1600.3.b.v.1151.6 | 6 | |||
120.107 | odd | 4 | 1600.3.b.w.1151.1 | 6 | |||
240.29 | odd | 4 | 1280.3.e.g.639.1 | 6 | |||
240.59 | even | 4 | 1280.3.e.h.639.1 | 6 | |||
240.149 | odd | 4 | 1280.3.e.i.639.6 | 6 | |||
240.179 | even | 4 | 1280.3.e.f.639.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
160.3.h.a.159.1 | ✓ | 6 | 15.14 | odd | 2 | ||
160.3.h.a.159.2 | yes | 6 | 12.11 | even | 2 | ||
160.3.h.b.159.5 | yes | 6 | 60.59 | even | 2 | ||
160.3.h.b.159.6 | yes | 6 | 3.2 | odd | 2 | ||
320.3.h.f.319.1 | 6 | 24.5 | odd | 2 | |||
320.3.h.f.319.2 | 6 | 120.59 | even | 2 | |||
320.3.h.g.319.5 | 6 | 24.11 | even | 2 | |||
320.3.h.g.319.6 | 6 | 120.29 | odd | 2 | |||
800.3.b.h.351.1 | 6 | 60.23 | odd | 4 | |||
800.3.b.h.351.6 | 6 | 15.8 | even | 4 | |||
800.3.b.i.351.1 | 6 | 15.2 | even | 4 | |||
800.3.b.i.351.6 | 6 | 60.47 | odd | 4 | |||
1280.3.e.f.639.1 | 6 | 48.5 | odd | 4 | |||
1280.3.e.f.639.6 | 6 | 240.179 | even | 4 | |||
1280.3.e.g.639.1 | 6 | 240.29 | odd | 4 | |||
1280.3.e.g.639.6 | 6 | 48.11 | even | 4 | |||
1280.3.e.h.639.1 | 6 | 240.59 | even | 4 | |||
1280.3.e.h.639.6 | 6 | 48.29 | odd | 4 | |||
1280.3.e.i.639.1 | 6 | 48.35 | even | 4 | |||
1280.3.e.i.639.6 | 6 | 240.149 | odd | 4 | |||
1440.3.j.a.1279.3 | 6 | 4.3 | odd | 2 | |||
1440.3.j.a.1279.4 | 6 | 5.4 | even | 2 | |||
1440.3.j.b.1279.3 | 6 | 1.1 | even | 1 | trivial | ||
1440.3.j.b.1279.4 | 6 | 20.19 | odd | 2 | inner | ||
1600.3.b.v.1151.1 | 6 | 120.53 | even | 4 | |||
1600.3.b.v.1151.6 | 6 | 120.83 | odd | 4 | |||
1600.3.b.w.1151.1 | 6 | 120.107 | odd | 4 | |||
1600.3.b.w.1151.6 | 6 | 120.77 | even | 4 |